The following references describe mathematical printing in the 1950s, before it became too expensive and degenerated into illegible typescript:

*The Printing of Mathematics* by T. W. Chaundy, P. R. Barrett and Charles Batey, Oxford University Press, 1954.

*Setting Mathematics* by Arthur Phillips, in *The Monotype Recorder* **40** (4), Winter 1956.

*Printing Mathematics* by Peter Basnett, in *Eureka* **23** (1960) 11-13.

*The Mathematician and the Printer. Hints on the preparation of mathematical and technical manuscripts.* by R. G. Hitchings, Hodgson, London, 1961.

*Copy-Editing*, The Cambridge Handbook for Editors, Authors, Publishers, by Judith Butcher, CUP. First edition 1975, second 1981, third 1992.

At that time, ordinary text (novels and newspapers) was set using the Linotype system, in which the compositor would use a huge keyboard to select characters and then they would be set in molten lead a whole line at a time.

However, this was unsuitable for mathematics and the "state of the art" was the Monotype Four Line System, which had movable type. The following piece of nonsense is a block provided by Monotype and used in the *Eureka* article:

Each letter is set on a block (shown in grey) that occupies space on one of the four lines. However, the $g$, $X$, $b$ and $Y$ overhang their blocks and are supported by spacer blocks (white) in the other line.

You could add big integral or summation signs in front of such a fractional expression, and (I think) a $d x$ vertically centered after it.

**PS on OCR (Optical Character Recognition)**

There is commercial software for OCR of maths but apparently no good FOSS. For ordinary text, *Tesseract-OCR* does a very good job, but its "equation" recognition seems to be limited. This article by Ray Smith of Google gives a good description of how it works.

There are comments on the Web asking for recognition of general LaTeX output or handwritten mathematics. These are fanciful because they are over-ambitious, not clearly defined and not what is actually required.

On the other hand there are huge numbers of old journal papers (increasingly available online as scans) that were printed with the technology described above, or less. It would be extremely valuable to be able to put these in digital form, for example for machine translation.

Anyone interested in a programming project (maybe contributing to tesseract) should therefore aim to recognise the Monotype "four line" formulae above. Of course it would also be necessary to recognise symbols, fonts, sub- and superscripts. All of these would appear to be within the design concept of tesseract.

Such a project should be regarded as a tool to *help* a human digitise the text, ie to reduce the amount of hand-editing that is needed but not necessarily eliminate it.

This post should be enough on its own to start such a project. More details of the old printing technologies are in the books and articles mention at the top of this post. I have copies of these that were kindly given to me (a long time ago) by David Tranah of CUP.